1. Field of the Invention
The present invention generally relates to processes for migrating seismic wave information and, more particularly, to processes for depth migration of seismic waves that contain rapid lateral velocity variations.
2. State of the Art
A primary goal of reflection seismology is to obtain accurate images of subsurface geological formations based upon surface recording of reflections of seismic waves that are purposefully directed into the earth. Toward that end, it is well known that seismic waves recorded by geophones or hydrophones at the earth's surface can be displayed as two-dimensional or three-dimensional seismic "time sections", each consisting of a large number of seismic traces. Although visual inspection of seismic time sections can intuitively suggest shapes and locations of subsurface reflecting formations, the visually-apparent images may be inaccurate or misleading. For example, when seismic information is recorded in geological media whose characteristics vary substantially in the horizontal direction, visual consideration of time sections can lead to erroneous conclusions as to the actual shapes and locations of subsurface reflectors. Accordingly, in practice, recorded seismic information usually is manipulated for the purpose of producing migrated sections that depict the proper spatial locations of subsurface reflectors.
Various geological conditions can cause lateral velocity variations in seismic waves. For example, overthrust zones can produce strong lateral velocity variations in seismic waves passing through the zones. Also, salt intrusion into sediments can cause substantial velocity variations in seismic waves that pass through the sediments.
Conventional time migration programs operate to focus diffracted energy to subsurface locations, but do not accurately account for rapid lateral velocity variations in seismic waves. The imaging programs that do account for lateral velocity variations caused by changes in geological media are, by way of distinction, called depth migration programs.
The results of seismic depth migration programs are normally based upon models of the geology being imaged. Therefore, when actual geological conditions differ substantially from conditions assumed within a given model, migration programs are likely to yield inaccurate results. In particular, the results provided by depth migration programs usually are sensitive to the particular seismic velocity models that are employed.
Seismic velocity models are normally based upon geological information, structural concepts, and upon analysis of the seismic data. In practice, velocity models are usually constructed separately from depth migration programs. However, the results of actual depth migrations are often considered, particularly during pre-stack procedures, for purposes of improving velocity models.
In current practice, time migration programs use one of three methods for time-migrating seismic data: the finite differencing method, the phase shift method, or the Kirchhoff method. Although these three methods can be extended for use in depth migration programs, the most common implementations of finite differencing methods cannot predict steeply sloping geological structures. The less commonly used "reverse time" finite differencing migration method can predict steeply sloping structures, but that method usually creates spurious reflection images when strong variations in seismic wave velocities exist. Also, the reverse-time method is computationally expensive.
In the Kirchhoff time migration method, a mapping is made of reflector positions that could cause energy to arrive on a particular wave trace at a particular time. Because time migration programs usually assume simple velocity variations, an analytical expression is sufficient for calculating the shapes of wavefronts. For example, the Dix equation can be employed for determining wavefront shapes when wave velocity through a geological media depends only on depth, and when large dips are not to be retained in the migrated images.
General closed-form analytical expressions do not exist, however, for use in the Kirchhoff method to provide accurate migration of seismic information derived from geological media that produce strong lateral velocity variations in seismic waves. In cases where there are strong lateral wave velocity variations in the seismic waves passing through such media, the Kirchhoff method is often extended beyond time migration by using standard ray tracing methods to construct wavefronts. The standard ray tracing methods fail, however, if there are multi-valued wavefronts and so-called shadow zones (i.e., zones where no rays pass), since those methods do not correctly describe interferences in multi-valued wavefronts. For example, standard ray tracing methods fail if a wavefront has a buried focus. Also, standard raypath methods erroneously predict rapidly varying, unbounded seismic wave amplitudes. Because multivalued wavefronts and shadow zones often occur in moderately complex geological structures, the practability of using standard raypath methods to extend the Kirchhoff method is limited.
Also in the seismology art, it is known to construct synthetic seismograms. A synthetic seismogram, generally speaking, is one produced by mathematical manipulations based upon models rather than by recording actual seismic reflections. Processes for constructing synthetic seismograms are sometimes referred to as forward modelling processes; one example of such a process is the Gaussian beam method.
The Gaussian beam method is known to be useful for modeling seismic energy in laterally varying geological media because that method overcomes many of the problems that are associated with other methods when dealing with shadow zones and multi-valued wavefronts. According to the Gaussian beam method, wavefields radiating from energy sources are computed by solving the wave equation using asymptotic expansions in ray-centered coordinates. The synthetic wavefields are constructed from acoustic energy source locations by adding beams of energy travelling in different directions, with each beam being a high-frequency solution to the wave equation. Normally, the synthetic wavefields are produced by computing a set of beams that simulate the acoustic energy source, propagating each of those beams to surface locations at which receivers are assumed to be located, and then summing the contributions from each of the propagated beams.